Transitioning the overlap of multiple objects
According to what you illustrated, I would propose a non-compositing way by using modifiers only:


Enter Edit Mode, Select one face as where the transition starts, ShiftS > Cursor to Selected to snap cursor to that face;
Select all faces, press Spacebar and search for Sort Mesh Elements, choose Cursor Distance in the popup menu, press F6 and toggle Reverse;
Create a duplication for the original object, repeat the last two steps on it, just leave Reverse untoggled;
Add Build modifier to the original object, toggle Reverse in the modifier stack;
Add a Wireframe modifier and a Build modifier to the duplicated object, leave Reverse untoggled this time.


After tweaking the modifier settings a bit, you will simply get something like this when playing animation:



Example file FYI.